Separating Subversion Forcing Axioms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916880969629696 |
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| author | Sakai, Hiroshi Switzer, Corey Bacal |
| author_facet | Sakai, Hiroshi Switzer, Corey Bacal |
| contents | We study a family of variants of Jensen's\emph{subcomplete forcing axiom}, $\mathsf{SCFA}$ and \emph{subproper forcing axiom}, $\mathsf{SubPFA}$. Using these we develop a general technique for proving non-implications of $\mathsf{SCFA}$, $\mathsf{SubPFA}$ and their relatives and give several applications. For instance we show that $\mathsf{SCFA}$ does not imply $\mathsf{MA}^+(σ$-closed$)$ and $\mathsf{SubPFA}$ does not imply Martin's Maximum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16276 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Separating Subversion Forcing Axioms Sakai, Hiroshi Switzer, Corey Bacal Logic We study a family of variants of Jensen's\emph{subcomplete forcing axiom}, $\mathsf{SCFA}$ and \emph{subproper forcing axiom}, $\mathsf{SubPFA}$. Using these we develop a general technique for proving non-implications of $\mathsf{SCFA}$, $\mathsf{SubPFA}$ and their relatives and give several applications. For instance we show that $\mathsf{SCFA}$ does not imply $\mathsf{MA}^+(σ$-closed$)$ and $\mathsf{SubPFA}$ does not imply Martin's Maximum. |
| title | Separating Subversion Forcing Axioms |
| topic | Logic |
| url | https://arxiv.org/abs/2308.16276 |